Orbiting spacecraft are used for a large variety of sensing and communication applications. For photographic purposes, it may be desirable for the spacecraft to be relatively near the Earth, so that the cameras or sensors are close to the subjects. For communication purposes, a geosynchronous equatorial orbit is often desirable. Whatever the orbit, a satellite must be stabilized in space if the sensors or antennas are to be pointed in appropriate directions.
Spacecraft attitude stabilization may be accomplished by spinning the spacecraft and by mounting the sensors or antennas on a despun platform. Alternatively, the spacecraft may be stabilized in three axes. Three-axis stabilization may be accomplished by a control system using fuel-burning thrusters, but the use of such thrusters requires the expenditure of fuel, which tends to limit the service life of the spacecraft. Another method for three-axis stabilization uses magnetic coils or torquers which interact with the magnetic fields of the heavenly body providing the desired torques. Magnetic torquers have the disadvantages that the available torques tend to be small, and undesirably dependent upon the local magnitude of the magnetic field of the heavenly body being orbited. The magnetic fields change from time to time and from location to location.
Larger torques than those available by the use of magnetic torquers may be achieved with electrically driven reaction wheels (RWA). Such wheels are also electrically driven and have the advantage of being able to provide relatively large torques regardless of orbital position.
In principle, a three-axis stabilized spacecraft requires only three mutually orthogonal, or non-planar, reaction wheels or momentum wheels. In order to provide for redundancy in the event that one of three orthogonal wheels should fail, spacecraft often include at least one additional reaction wheel, oriented such that it is non-planar with any other two RWAs. The fourth wheel provides redundancy for all three wheels. Thus, the fourth wheel may be used in conjunction with two of the other wheels to control the spacecraft attitude.
In addition, increased expectations relating to the performance of spacecraft and improved capabilities have led to a continuing increase in the size of spacecraft. This increased size in turn requires greater torque and momentum capability along each control axis. Rather than use three reaction wheels with a fourth wheel, aside from redundancy, it has been found that there are advantages to using four or more skewed smaller reaction wheels to obtain the required momentum and torque. When four or more reaction wheels are used, modern control techniques utilize all the wheels during operation.
During attitude control operations, the various RWAs are accelerated and decelerated to apply torques to the spacecraft body. In this process the RWAs, and thus the spacecraft accumulate momentum over time. The vector sum of all the RWA momentum is referred as the total spacecraft momentum.
In cases where number of wheels is four or more, the total spacecraft momentum can be stored in the set of wheels in infinitely many ways due to the under-determined nature of the problem, or the existence of the wheel null-space. For example, one way to distribute zero momentum is to have every wheel spin at zero speed. Another way is to have all the wheels spin at non-zero speeds such that the set of speeds form a wheel speed null vector, or the vector sum of all the individual wheel momentums is zero.
Prior art speed management arrangements drove the wheel speeds toward power optimal values. In these prior art arrangements, the net momentum is distributed such that the square root of the sum of the squares of all the individual wheel momentums/speeds is minimized. This is also equivalent to minimization of the 2-norm of the speed vector, or to having zero components of the wheel speed vector along the null-space.
In systems implementing RWAs for attitude control, a wheel may reach its maximum speed, even though the total wheel stored momentum is small. This requires periodic momentum dumping by firing thrusters from time to time. It is desirable to prolong periods between momentum-dumping maneuvers in order to reduce operational efforts and thruster fuel expenditure. In cases where the number of wheels is four or greater, a given amount of momentum in the spacecraft body coordinate frame can be stored in the set of wheels in infinitely many ways due to the existence of wheel speed null space. In the prior art, the net momentum is distributed such that the square root of the sum of the squares of all the individual wheel momentums/speeds is minimized. This is also equivalent to minimization of the 2-norm of the speed vector, or to having zero components of the wheel speed vector along the null-space.
For example, described in U.S. Pat. No. 5,058,835 issued Oct. 22, 1991 to Goodzeit et al. entitled WHEEL SPEED MANAGEMENT CONTROL SYSTEM FOR SPACECRAFT is a system of wheel speed management for a spacecraft that uses at least four reaction wheels for attitude control. This system monitors the wheel speeds and generates a wheel speed error vector. The error vector is integrated, and the error vector and its integral are combined to form a correction vector. The correction vector is summed with the attitude control torque command signals for driving the reaction wheels. An improvement disclosed in U.S. Pat. No. 6,141,606 issued Oct. 31, 2000 to Reckdahl entitled WHEEL SPEED CONTROL SYSTEM FOR A SPACECRAFT WITH REJECTION OF NULL SPACE WHEEL MOMENTUM controls wheel speed nullspace components instead of wheel speed errors.
These systems are effective to maintain each reaction wheel at its power optimal speed so as to keep the total wheel proven minimum. Both are based on minimization of the 2-norm RWA speeds to reduce RWA energy requirements. The drawback of the methods is that simply minimizing maximum energy into the system does not minimize the maximum speed of the fastest of the reaction wheels, and hence does not provide the longest possible periods between momentum dumping maneuvers. This results in more than necessary fuel consumption and active ground involvement.
Desired is an improvement, in which the maximum angular speeds of all the reaction wheels are minimized, so that momentum dumping is least frequently carried out, and concomitant fuel consumption and ground involvement minimized.